One form of generally employed operating procedure for removing water from sludge such as that which is produced in a sewage treatment installation involves adding an organic or inorganic flocculating agent or a filtering aid and then removing the water in chamber-type filter presses. In chamber-type filter presses of the usual design configuration the sludge is fed into filter chambers which are closed on all sides and the medium from which water is to be removed continues to be pumped, by means of pumps, under high pressure, until the desired content of dry substance is attained. In that procedure, the filtrate contained in the medium from which water is to be removed is discharged through the separation walls of the individual filter chambers, such walls consisting of filter material. A disadvantage of known chamber filter presses of that kind and the corresponding operating procedure involved in the removal of water is that, while involving a very high level of technical expenditure, the efficiency with which the pressure is transmitted to the sludge from which water is to be removed decreases from one chamber to another in the direction of conveying movement. Furthermore the hydrostatic pressure for removing water is built up by pumps, and that gives rise to the serious disadvantage that flocculation of the sludge, which is achieved by use of a flocculating agent or other filtering aid, is destroyed again in the pumping phase. Another disadvantage lies in the discontinuous mode of operation of such chamber filter presses as the feed of sludge has to be interrupted when the sludge chamber is opened. Furthermore the entire water-removal procedure including the preliminary step in removing water is effected at low pressure in the chamber which is designed for high pressures so that the chamber is used in a highly uneconomical fashion.